On the α-spectral radius of the k-uniform supertrees.

Let G be a k-uniform hypergraph with vertex set V (G) and edge set E(G). A connected and acyclic hypergraph is called a supertree. For 0 ≤ α < 1, the α-spectral radius of G is the largest H-eigenvalue of αD(G) + (1 − α)A(G), where D(G) and A(G) are the diagonal tensor of the degrees and the adjacency tensor of G, respectively. In this paper, we determine the unique supertrees with maximum α-spectral radius among all k-uniform supertrees with m edges and independence number β for ⌈m(k−1)+1 k ⌉≤ β ≤ m, among all k-uniform supertrees with given degree sequences, and among all k-uniform supertrees with m edges and matching number μ for 1 ≤ μ ≤⌊m(k−1)+1 k ⌋, respectively. [ABSTRACT FROM AUTHOR]